# Question about photons/neutrinos/SOL
**URL:** https://boards.straightdope.com/t/question-about-photons-neutrinos-sol/605608
**Category:** Factual Questions
**Created:** [December 9, 2011, 11:44am UTC](https://boards.straightdope.com/t/question-about-photons-neutrinos-sol/605608 "2011-12-09T11:44:39Z")
**Posts on this page:** 13
**Page:** 1
### Author:  [@kaltkalt](https://boards.straightdope.com/u/kaltkalt)
#### Post date: [December 9, 2011, 11:44am UTC](https://boards.straightdope.com/t/question-about-photons-neutrinos-sol/605608/1 "2011-12-09T11:44:39Z")
I don’t see how a photon can be truly massless. It has energy (so E=M…), it can transfer that energy to atoms, and solar sails work by being pushed by photons (momentum). Photons don’t go zipping through solid things the way neutrinos do (billions going through you and through the earth right this second), and when photons do go through something transparent, they slow down greatly (i.e. the speed of light through, say, clear glass or water is significantly slower than the SOL through a vacuum.
I’m sure the mass of a photon, if it has any, is ridiculously small - no question about that. But maybe the reason we’re detecting these superluminal neutrinos is that the ultimate relativistic speed limit is not the speed of light but rather the speed of neutrinos, which are in fact truly massless, and the speed of light (i.e. photons) is a wee tiny bit slower than that because they have a minuscule amount of mass, thus limiting their speed to something slightly less than that of massless neutrinos… say 99.999999999999% the speed of neutrinos.
I have read the standard wikipedia entry about photons, among other things, and while the standard answer is they are massless, upon further reading it seems we are just pretty sure they are massless. If they have mass, it would be an extremely small amount.
And if photons do have mass, maybe all that “dark matter” is really just the collective mass of all the photons zooming around the universe at 99.999999999999% the speed of neutrinos. Even if photons have the most minuscule amount of mass, think how many are zooming around the universe from every star from the beginning of time.
Note: I know that the superluminal neutrinos are not confirmed yet and I know that’s being discussed/debated here on other threads - it’s not my intent or desire to debate that here… so just for the sake of my question let’s presume the tests have been confirmed and (slightly) superluminal neutrinos actually do exist.
Can someone who knows more about physics than I do give me a good reason why my theory (if you can even call it that) is wrong? Thanks.
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### Author:  [@CalMeacham](https://boards.straightdope.com/u/CalMeacham)
#### Post date: [December 9, 2011, 12:55pm UTC](https://boards.straightdope.com/t/question-about-photons-neutrinos-sol/605608/2 "2011-12-09T12:55:22Z")
There’s nothing inconsistent with a massless photon being able to convey momentum. It certainly goes against everyday experience – in order to convey momentum on the macro level, something does indeed have to have mass. But there are plenty of examples of things that work on the quantum level in a way contrary to experience or expectation in our macro human everyday experience. Your lack of comfort with massless photons is understandable, but doesn’t rule out their existence any more than the non-existence of macrioscopic tunnelling phenomena rules out the existence of tunnel diodes or schroedinger’s equation.
If you’ve read the Wikipedia page on _photons_, then you encountered the discussion on limits to photon mass. I was very surprised by an article I read in _Scientific American_ back in the 1970s on the implications of a photon with mass. As they note, it would alter Maxwell’s equations and there are certainly tests you can make for such a mass. The thing is, all such tests that have been done still relegate the photon’s rest mass – if there is any – to a tiny value, and the effects are still not visible to us. The conclusion is that photons really _are_ masless, or their mass is so small that it is still beyond our detection, and make no difference to even our most sensitive dealings with the quantum world than if they had mass.
> [@](#):
>
> Experimental checks on photon mass
>
> The photon is currently understood to be strictly massless, but this is an experimental question. If the photon is not a strictly massless particle, it would not move at the exact speed of light in vacuum, c. Its speed would be lower and depend on its frequency. Relativity would be unaffected by this; the so-called speed of light, c, would then not be the actual speed at which light moves, but a constant of nature which is the maximum speed that any object could theoretically attain in space-time.[21] Thus, it would still be the speed of space-time ripples (gravitational waves and gravitons), but it would not be the speed of photons.
>
> A massive photon would have other effects as well. Coulomb’s law would be modified and the electromagnetic field would have an extra physical degree of freedom. These effects yield more sensitive experimental probes of the photon mass than the frequency dependence of the speed of light. If Coulomb’s law is not exactly valid, then that would cause the presence of an electric field inside a hollow conductor when it is subjected to an external electric field. This thus allows one to test Coulomb’s law to very high precision.[22] A null result of such an experiment has set a limit of m ≲ 10−14 eV/c2.[23]
>
> Sharper upper limits have been obtained in experiments designed to detect effects caused by the Galactic vector potential. Although the galactic vector potential is very large because the galactic magnetic field exists on very long length scales, only the magnetic field is observable if the photon is massless. In case of a massive photon, the mass term would affect the galactic plasma. The fact that no such effects are seen implies an upper bound on the photon mass of m \< 3×10−27 eV/c2.[24] The galactic vector potential can also be probed directly by measuring the torque exerted on a magnetized ring.[25] Such methods were used to obtain the sharper upper limit of 10−18eV/c2 given by the Particle Data Group.[26]
>
> These sharp limits from the non-observation of the effects caused by the galactic vector potential have been shown to be model dependent.[27] If the photon mass is generated via the Higgs mechanism then the upper limit of m≲10−14 eV/c2 from the test of Coulomb’s law is valid.
>
> Photons inside superconductors do develop a nonzero effective rest mass; as a result, electromagnetic forces become short-range inside superconductors.
> **[Photon](https://en.wikipedia.org/wiki/Photon)**
>
> A photon (from Ancient Greek φῶς, φωτός (phôs, phōtós) 'light') is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless particles that can move no faster than the speed of light measured in vacuum. The photon belongs to the class of boson particles.
> As with other elementary particles, photons are best explained by quantum mechanics and ex...
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### Author:  [@Nancarrow](https://boards.straightdope.com/u/Nancarrow)
#### Post date: [December 9, 2011, 1:14pm UTC](https://boards.straightdope.com/t/question-about-photons-neutrinos-sol/605608/3 "2011-12-09T13:14:01Z")
> [@kaltkalt](#):
>
> I don’t see how a photon can be truly massless. It has energy (so E=M…), it can transfer that energy to atoms, and solar sails work by being pushed by photons (momentum).
I’ll just address this bit, don’t really know about the rest. Okay here’s the edgy bit:
E=mc^2 is wrong.
Here’s the non-edgy version. It’s not wrong, it’s a special case of a more general equation, the energy-momentum relation,
E^2 = (m^2) (c^4) +(p^2)(c^2)
(p=momentum)
So you can’t say ‘if something has energy it must have mass’. The converse is true - anything with mass must have energy - but something (cough_photon_cough) can have energy and no mass, as long as it has momentum. Obviously, the Newtonian definitions of p=mv and kinetic E=(1/2)mv^2 no longer work in quite the same way. Although it can be shown that the rest energy mc^2 and the classical K.E are the first two terms you get if you do a binomial expansion on the E-M relation, which shows one way in which Newtonian concepts ‘work’ for low velocities.
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### Author:  [@Exapno\_Mapcase](https://boards.straightdope.com/u/Exapno_Mapcase)
#### Post date: [December 9, 2011, 4:23pm UTC](https://boards.straightdope.com/t/question-about-photons-neutrinos-sol/605608/4 "2011-12-09T16:23:02Z")
> [@kaltkalt](#):
>
> I’m sure the mass of a photon, if it has any, is ridiculously small - no question about that. But maybe the reason we’re detecting these superluminal neutrinos is that the ultimate relativistic speed limit is not the speed of light but rather the speed of neutrinos, which are in fact truly massless, and the speed of light (i.e. photons) is a wee tiny bit slower than that because they have a minuscule amount of mass, thus limiting their speed to something slightly less than that of massless neutrinos… say 99.999999999999% the speed of neutrinos.
Here’s one more problem. We know that neutrinos do have mass. The possible superluminal neutrinos therefore can’t be explained away as being massless. (Though it looks more and more that they were never superluminal at all.)
And dark matter behaves in a variety of specific ways that’s totally incompatible with the behavior of photons. Of all the many explanations possible, photons have to be close to the bottom.
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### Author:  [@kaltkalt](https://boards.straightdope.com/u/kaltkalt)
#### Post date: [December 9, 2011, 4:23pm UTC](https://boards.straightdope.com/t/question-about-photons-neutrinos-sol/605608/5 "2011-12-09T16:23:54Z")
Thanks for the info.
Are we _sure_ energy has no mass? Might that depend on the existence of the Higgs? No question that mass has energy. Why wouldn’t pure energy have mass? It’s pretty hard to weigh a ball of pure energy, of course. QUESTION: Does a charged AA battery weigh ever so slightly more than a completely depleted one? (i realize that’s chemical energy, but energy is energy).
If photons DID have some small mass, would that explain the superluminal neutrinos and possibly dark matter? Could the momentum/pressure of all those photons out in the universe explain expansion? Actually that apparently wouldn’t depend on whether or not photons had mass or not, light has radiation pressure… though that too would be easier to explain if light had some mass.
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### Author:  [@Exapno\_Mapcase](https://boards.straightdope.com/u/Exapno_Mapcase)
#### Post date: [December 9, 2011, 5:00pm UTC](https://boards.straightdope.com/t/question-about-photons-neutrinos-sol/605608/6 "2011-12-09T17:00:33Z")
Radiation pressure is momentum.
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### Author:  [@Chronos](https://boards.straightdope.com/u/Chronos)
#### Post date: [December 9, 2011, 7:48pm UTC](https://boards.straightdope.com/t/question-about-photons-neutrinos-sol/605608/7 "2011-12-09T19:48:20Z")
> [@](#):
>
> QUESTION: Does a charged AA battery weigh ever so slightly more than a completely depleted one? (i realize that’s chemical energy, but energy is energy).
Yes. But it’s not so much that energy _is_ mass, as that (for lack of a better way of describing it) mass is a way of arranging energy. To clarify: The energy of a system depends on what reference frame you’re looking at it in. If I have a ball sitting on a tabletop, one might say that it has zero kinetic energy. But then, one might also point out that, due to the rotation of the Earth, it’s zipping around at close to a thousand miles an hour, and so in that reference frame it has a pretty significant kinetic energy. And of course in either case it has the same non-kinetic energy, whatever that might be, so the total energy varies by reference frame.
But no matter what reference frame I look at that ball in, there’s some minimum amount of energy, such that the ball’s total energy will never be less than that minimum. That portion of the energy that you can’t get rid of by going to a different reference frame is what we call the mass.
> [@](#):
>
> If photons DID have some small mass, would that explain the superluminal neutrinos and possibly dark matter? Could the momentum/pressure of all those photons out in the universe explain expansion? Actually that apparently wouldn’t depend on whether or not photons had mass or not, light has radiation pressure… though that too would be easier to explain if light had some mass.
We can’t rule out photons having a very small but nonzero mass, but we can say that if they do, that mass is very, very small, by far small enough that it’s a negligible part of the photon’s total energy. In the very early stages of the Universe, the energy in photons was a significant portion of the Universe’s total energy content, and had significant effects on the evolution of the Universe. That era is long past, though, and now the energy in photons makes up only a tiny, tiny proportion of the total energy content, so small that it’s almost always ignored completely in calculations.
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### Author:  [@Candyman74](https://boards.straightdope.com/u/Candyman74)
#### Post date: [December 9, 2011, 8:19pm UTC](https://boards.straightdope.com/t/question-about-photons-neutrinos-sol/605608/8 "2011-12-09T20:19:46Z")
Related question for the physicists.
People often use e=mc^2 in such debates. My question is this: this does not mean that energy IS mass, does it? Just that it is _equivalent_ to mass x c^2.
i.e. - It’s not identical to; it’s equivalent to.
The reason I ask is that from time to time I’ll see a debate where energy and mass are discussed by non-physicists, and the assumption sometimes seems to be that the equation means that the two are the same thing (“energy IS mass!”). I always want to say “No, they’re not the same thing. Look at them! They’re clearly different!” but don’t want to do so unless I’m right in doing so. And knowing me, I’m probably wrong.
As I understand it, the two can be exchanged by certain processes (wood can be burned, etc.) and the values are defined by that equation. But that doesn’t mean wood\* is\* thermal energy, just that it can be put through a process which converts it to such.
Sorry if this sounds like a stupidly elementary question.
There’s a followup, though: what about the reverse? Obviously you can’t take some thermal energy and turn it into wood. But what reverse processes, if any, are there?
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### Author:  [@Asympotically\_fat](https://boards.straightdope.com/u/Asympotically_fat)
#### Post date: [December 9, 2011, 8:25pm UTC](https://boards.straightdope.com/t/question-about-photons-neutrinos-sol/605608/9 "2011-12-09T20:25:31Z")
> [@Candyman74](#):
>
> Related question for the physicists.
>
> People often use e=mc^2 in such debates. My question is this: this does not mean that energy IS mass, does it? Just that it is _equivalent_ to mass x c^2.
>
> i.e. - It’s not identical to; it’s equivalent to.
>
> The reason I ask is that from time to time I’ll see a debate where energy and mass are discussed by non-physicists, and the assumption sometimes seems to be that the equation means that the two are the same thing. I always want to say “No, they’re not the same thing. Look at them! They’re clearly different!” but don’t want to do so unless I’m right in doing so.
>
> As I understand it, the two can be exchanged by certain processes (wood can be burned, etc.) and the values are defined by that equation. But that doesn’t mean wood\* is\* thermal energy, just that it can be put through a process which converts it to such.
>
> Sorry if this sounds like a stupidly elementary question.
>
> There’s a followup, though: what about the reverse? Obviously you can’t take some thermal energy and turn it into wood. But what reverse processes, if any, are there?
E = mc[sup]2[/sup] relates the rest energy of an system E (though it’s probably preferable to right it as E[sub]rest[/sub]) to it’s (rest) mass.
Energy and mass are very closely related concepts in relativity both of which can be defined by the 4-momentum vector.
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### Author:  [@Candyman74](https://boards.straightdope.com/u/Candyman74)
#### Post date: [December 9, 2011, 8:33pm UTC](https://boards.straightdope.com/t/question-about-photons-neutrinos-sol/605608/10 "2011-12-09T20:33:19Z")
> [@These are my own pants](#):
>
> E = mc[sup]2[/sup] relates the rest energy of an system E (though it’s probably preferable to right it as E[sub]rest[/sub]) to it’s (rest) mass.
>
> Energy and mass are very closely related concepts in relativity both of which can be defined by the 4-momentum vector.
I’m sure that probably answers my question. Unfortunately, it does not do so in a language I can understand. Got the layman version? 🙂
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### Author:  [@kaltkalt](https://boards.straightdope.com/u/kaltkalt)
#### Post date: [December 10, 2011, 6:08am UTC](https://boards.straightdope.com/t/question-about-photons-neutrinos-sol/605608/11 "2011-12-10T06:08:41Z")
Dollars are not Pesos, but Dollars = Pesos(X) where X is the current exchange rate. I’ve always thought that’s an analogy of energy and mass, just with a nonvariable exchange rate (C^2). Is that a bad analogy, and if so why?
Chronos: I’m gonna have to contemplate your example about the ball and minimum relative kinetic energy. Interesting explanation.
If a photon does have a trivial amount of mass and a neutrino does not, would/could that explain the superluminal neutrino observations? This is really my core question.
As a sidenote, I also don’t understand how something (i.e. a photon) can have momentum if it has no mass. I’ve read explanations but none that make any sense to me. I like analogies, but I’m afraid there probably is no analogy that could explain this. Momentum = mass x velocity, and that makes perfect sense to me. I realize that is classical mechanics, but momentum without mass must mean something totally different.
thanks
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### Author:  [@Exapno\_Mapcase](https://boards.straightdope.com/u/Exapno_Mapcase)
#### Post date: [December 10, 2011, 4:21pm UTC](https://boards.straightdope.com/t/question-about-photons-neutrinos-sol/605608/12 "2011-12-10T16:21:17Z")
> [@kaltkalt](#):
>
> As a sidenote, I also don’t understand how something (i.e. a photon) can have momentum if it has no mass. I’ve read explanations but none that make any sense to me. I like analogies, but I’m afraid there probably is no analogy that could explain this. Momentum = mass x velocity, and that makes perfect sense to me. I realize that is classical mechanics, but momentum without mass must mean something totally different.
I’m not sure how to explain this, but it’s important to repeat the equation given above.
E[sup]2[/sup] = (m[sup]2[/sup]) (c[sup]4[/sup]) +(p[sup]2[/sup])(c[sup]2[/sup])
We’ve had the shorthand that E=mc[sup]2[/sup] drummed into us for so long that in our heads we subconsciously assume that energy is the same thing as mass. And that’s true for us and the world we experience.
But the equation tells us immediately that Energy is built up of two components, mass and momentum (p). If the mass is zero, one side of the equation goes to zero but the other side remains. If momentum is zero, one side of the equation goes to zero but the other side remains. That’s surprising, especially in classical terms, and it’s also confusing.
For most practical purposes talking about energy being equal to or convertible into mass makes good shorthand sense. It’s not strictly true, but no shorthand is ever strictly true. It only matters when it matters. In the one case of massless particles it matters very much. Then have momentum - they must because they cannot exist at rest - and that is energy and so that defines how they interact with other particles.
The shorthand answer for not allowing photons to have mass is that even if it would explain this one totally anomalous observation, it would screw up the known results of a billion other observations. You’d have to plug that mass into the equation I gave and see what the new results are. And those would be wrong for every other single thing ever measured.
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### Author:  [@Chronos](https://boards.straightdope.com/u/Chronos)
#### Post date: [December 10, 2011, 9:11pm UTC](https://boards.straightdope.com/t/question-about-photons-neutrinos-sol/605608/13 "2011-12-10T21:11:12Z")
> [@](#):
>
> If a photon does have a trivial amount of mass and a neutrino does not, would/could that explain the superluminal neutrino observations? This is really my core question.
No, it could not. The fundamental speed limit c (which may or may not be the speed of light) is known too precisely to be consistent with this interpretation.